Statistics • Organizing and Graphing Data
Enter raw quantitative data and this tool will build a grouped frequency distribution and its cumulative version: cumulative frequency, cumulative relative frequency, and cumulative percentage. It also draws the ogive (cumulative frequency graph) using class boundaries on the horizontal axis.
A cumulative frequency distribution lists the running total of frequencies up to each class, showing how many observations are at or below each upper class boundary. It helps answer questions like how many values are less than or equal to a given cutoff.
If class frequencies are f1, f2, ..., fk in order, the cumulative frequency for class j is Fj = f1 + f2 + ... + fj. The last cumulative frequency equals the total number of observations.
With total N, cumulative relative frequency for class j is Fj / N. Cumulative percentage is (Fj / N) x 100, and it increases from about 0% up to about 100% (allowing for rounding).
An ogive is the cumulative frequency graph created by plotting cumulative frequencies against upper class boundaries and connecting the points with line segments. It allows approximate cumulative counts or proportions to be read for values along the horizontal axis.
Fewer classes give a simpler summary, while more classes show more detail but can look jagged. Leaving the number of classes blank lets the calculator choose an automatic value in a typical range.